Bottom Line:
We increase complexity from simple opinion adaptation processes studied in earlier research to more complex decision-making determined by costs and benefits, and from bilateral to multilateral cooperation.We find some empirical support for our main results: Our model develops a bimodal coalition size distribution over time similar to those found in social structures.Our detection and distinguishing of phase transitions may be exemplary for other models of socio-economic systems with low agent numbers and therefore strong finite-size effects.

ABSTRACTComplex networks describe the structure of many socio-economic systems. However, in studies of decision-making processes the evolution of the underlying social relations are disregarded. In this report, we aim to understand the formation of self-organizing domains of cooperation ("coalitions") on an acquaintance network. We include both the network's influence on the formation of coalitions and vice versa how the network adapts to the current coalition structure, thus forming a social feedback loop. We increase complexity from simple opinion adaptation processes studied in earlier research to more complex decision-making determined by costs and benefits, and from bilateral to multilateral cooperation. We show how phase transitions emerge from such coevolutionary dynamics, which can be interpreted as processes of great transformations. If the network adaptation rate is high, the social dynamics prevent the formation of a grand coalition and therefore full cooperation. We find some empirical support for our main results: Our model develops a bimodal coalition size distribution over time similar to those found in social structures. Our detection and distinguishing of phase transitions may be exemplary for other models of socio-economic systems with low agent numbers and therefore strong finite-size effects.

f2: Acquaintance network with coalition structure (each color represents one coalition, black dots are singleton coalitions) for varying system size (columns: N = 300, N = 600 and N = 900) and adaptation rate (rows: ϕ = 0.97 and ϕ = 0.1). Note that some of the smaller network components consist of more than one coalition. Each network is the equilibrium result of one model run.

Mentions:
For the case of agents exploiting a common pool resource7, we find a second order phase transition when adaptation versus coalition formation crosses its critical value, ϕ = ϕc. For subcritical adaptation rates (see Methods for the description of the model and parameters), the coalition structure is dominated by very few macroscopic or even near-global coalitions. This leads to a peculiarly multimodal size distribution that can also be observed in various real-world systems8910111213, not only in socio-economic contexts but also in purely physical systems such as droplets14. In contrast, at the critical adaptation rate, a more heterogeneous but power-law-tailed size distribution with much smaller maximal coalitions emerges (see Figs 2 and 3).

f2: Acquaintance network with coalition structure (each color represents one coalition, black dots are singleton coalitions) for varying system size (columns: N = 300, N = 600 and N = 900) and adaptation rate (rows: ϕ = 0.97 and ϕ = 0.1). Note that some of the smaller network components consist of more than one coalition. Each network is the equilibrium result of one model run.

Mentions:
For the case of agents exploiting a common pool resource7, we find a second order phase transition when adaptation versus coalition formation crosses its critical value, ϕ = ϕc. For subcritical adaptation rates (see Methods for the description of the model and parameters), the coalition structure is dominated by very few macroscopic or even near-global coalitions. This leads to a peculiarly multimodal size distribution that can also be observed in various real-world systems8910111213, not only in socio-economic contexts but also in purely physical systems such as droplets14. In contrast, at the critical adaptation rate, a more heterogeneous but power-law-tailed size distribution with much smaller maximal coalitions emerges (see Figs 2 and 3).

Bottom Line:
We increase complexity from simple opinion adaptation processes studied in earlier research to more complex decision-making determined by costs and benefits, and from bilateral to multilateral cooperation.We find some empirical support for our main results: Our model develops a bimodal coalition size distribution over time similar to those found in social structures.Our detection and distinguishing of phase transitions may be exemplary for other models of socio-economic systems with low agent numbers and therefore strong finite-size effects.

ABSTRACTComplex networks describe the structure of many socio-economic systems. However, in studies of decision-making processes the evolution of the underlying social relations are disregarded. In this report, we aim to understand the formation of self-organizing domains of cooperation ("coalitions") on an acquaintance network. We include both the network's influence on the formation of coalitions and vice versa how the network adapts to the current coalition structure, thus forming a social feedback loop. We increase complexity from simple opinion adaptation processes studied in earlier research to more complex decision-making determined by costs and benefits, and from bilateral to multilateral cooperation. We show how phase transitions emerge from such coevolutionary dynamics, which can be interpreted as processes of great transformations. If the network adaptation rate is high, the social dynamics prevent the formation of a grand coalition and therefore full cooperation. We find some empirical support for our main results: Our model develops a bimodal coalition size distribution over time similar to those found in social structures. Our detection and distinguishing of phase transitions may be exemplary for other models of socio-economic systems with low agent numbers and therefore strong finite-size effects.